Answer:
y = 0.019x - 7
32.9 therms
0.019 therms
1.9 therms
Step-by-step explanation:
Given the following :
X =size of house (sq ft)
Y = Amount of natural gas used
The general form of a some linear regression model :
y = ßx + a
Where ;
ß = slope or gradient
x = independent variable
y = predicted value
a = y- intercept value
(A)
If ß = slope of population regression line = 0.019
a = y intercept of population regression line = -7
The regression model could be expressed as :
y = 0.019x + (-7)
y = 0.019x - 7
(B)What is the mean value of gas usage for houses with 2100 sq ft of space?
Here x = 2100 sq ft ; Inputting the value of x into the regression equation:
y = 0.019x - 7
y = 0.019(2100) - 7
y = 39.9 - 7
y = 32.9 therms
C) What is the average change in usage associated with a 1 square foot increase in size?
Change in usage associated with change in size can be gotten from :
ßx, where, ß change in y with respect to x ;
x = 1 square foot
ß = 0.019
Change = 0.019*(1) = 0.019 therms
(d) What is the average change in usage associated with a 100 square feet increase in size?
ßx, where, ß change in y with respect to x ;
x = 100 square feet
ß = 0.019
Change = 0.019*(100) = 1.9 therms
